Square root 6 is the answe
The larger of two numbers exceeds twice the smaller by one. The system of equations are y = 2x + 1 and y + 6 = 3x. So option 2 is correct
<u>Solution:</u>
Given, y is the larger number and x be the smaller number.
We have to find which of the given systems of equations represents the word problem?
Now, the larger of two numbers exceeds twice the smaller by one.
Then, y – (2 × x) = 1 ⇒ y – 2x = 1 ⇒ y = 2x + 1
And, three times the smaller exceeds the larger by six
Then, 3 × x – y = 6 ⇒ 3x – y = 6 ⇒ y + 6 = 3x
Hence, the system of equations are y = 2x + 1 and y + 6 = 3x. so option 2 is correct.
Assume that the initial coordinates are (x,y) and that the dilated coordinates are (x',y').
The dilation is therefore:
(x,y) ............> (x',y')
Now, let's assume that the dilation factor is k.
Therefore:
x' = kx
y' = ky
Based on the above, all the student has to do is get the initial coordinates and the final ones and then substitute in any of the above two equations to get the value of k.
Example:
Assume an original point at (2,4) is dilated to coordinates (4,8). Find the dilation factor.
Assume the dilation coefficient is k.
(x,y) are (2,4) and (x',y') are (4,8)
Therefore:
x' = kx .........> 4 = k*2 ..........> k = 2
or:
y' = ky ..........> 8 = k*4 .........> k = 2
Based on the above, the dilation coefficient would be 2.
Hope this helps :)
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Step-by-step explanation:
Answer:
C = 13
Step-by-step explanation:
A²+B²=C²
where c is the hypothenuse
5²+12²=c²
25+144=c²
169=c²
√169 = c
13 = c
